Solve 3/5x-[7/4(x/5+1/2)]=frac{7}{3}y-frac{5}{4}

$$\frac { 3 } { 5 } x - [ \frac { 7 } { 4 } ( \frac { x } { 5 } + \frac { 1 } { 2 } ) ] = \frac { 7 } { 3 } y - \frac { 5 } { 4 }$$

Solve for x

$$x=\frac{28y}{3}-\frac{3}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 5,4,2,3.

$$36x-105\left(\frac{x}{5}+\frac{1}{2}\right)=140y-75$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{x}{5} times \frac{2}{2}. Multiply \frac{1}{2} times \frac{5}{5}.

$$36x-105\left(\frac{2x}{10}+\frac{5}{10}\right)=140y-75$$

Since \frac{2x}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$36x-105\times \frac{2x+5}{10}=140y-75$$

Express 105\times \frac{2x+5}{10} as a single fraction.

$$36x-\frac{105\left(2x+5\right)}{10}=140y-75$$

Use the distributive property to multiply 105 by 2x+5.

$$36x-\frac{210x+525}{10}=140y-75$$

Divide each term of 210x+525 by 10 to get 21x+\frac{105}{2}.

$$36x-\left(21x+\frac{105}{2}\right)=140y-75$$

To find the opposite of 21x+\frac{105}{2}, find the opposite of each term.

$$36x-21x-\frac{105}{2}=140y-75$$

Combine 36x and -21x to get 15x.

$$15x-\frac{105}{2}=140y-75$$

Add \frac{105}{2} to both sides.

$$15x=140y-75+\frac{105}{2}$$

Add -75 and \frac{105}{2} to get -\frac{45}{2}.

$$15x=140y-\frac{45}{2}$$

Divide both sides by 15.

$$\frac{15x}{15}=\frac{140y-\frac{45}{2}}{15}$$

Dividing by 15 undoes the multiplication by 15.

$$x=\frac{140y-\frac{45}{2}}{15}$$

Divide 140y-\frac{45}{2} by 15.

$$x=\frac{28y}{3}-\frac{3}{2}$$

Solve for y

$$y=\frac{3x}{28}+\frac{9}{56}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 5,4,2,3.

$$36x-105\left(\frac{x}{5}+\frac{1}{2}\right)=140y-75$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{x}{5} times \frac{2}{2}. Multiply \frac{1}{2} times \frac{5}{5}.

$$36x-105\left(\frac{2x}{10}+\frac{5}{10}\right)=140y-75$$

Since \frac{2x}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$36x-105\times \frac{2x+5}{10}=140y-75$$

Express 105\times \frac{2x+5}{10} as a single fraction.

$$36x-\frac{105\left(2x+5\right)}{10}=140y-75$$

Use the distributive property to multiply 105 by 2x+5.

$$36x-\frac{210x+525}{10}=140y-75$$

Divide each term of 210x+525 by 10 to get 21x+\frac{105}{2}.

$$36x-\left(21x+\frac{105}{2}\right)=140y-75$$

To find the opposite of 21x+\frac{105}{2}, find the opposite of each term.

$$36x-21x-\frac{105}{2}=140y-75$$

Combine 36x and -21x to get 15x.

$$15x-\frac{105}{2}=140y-75$$

Swap sides so that all variable terms are on the left hand side.

$$140y-75=15x-\frac{105}{2}$$

Add 75 to both sides.

$$140y=15x-\frac{105}{2}+75$$

Add -\frac{105}{2} and 75 to get \frac{45}{2}.

$$140y=15x+\frac{45}{2}$$

Divide both sides by 140.

$$\frac{140y}{140}=\frac{15x+\frac{45}{2}}{140}$$

Dividing by 140 undoes the multiplication by 140.

$$y=\frac{15x+\frac{45}{2}}{140}$$

Divide 15x+\frac{45}{2} by 140.

$$y=\frac{3x}{28}+\frac{9}{56}$$